Phys11 Temperature&Heat

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Module 9

Temperature and Heat



Temperature We associate the concept of temperature with

how hot or cold an object feels

Our senses provide us with a qualitativeindication of temperature

Our senses are unreliable for this purpose

We need a reliable and reproducible method

for measuring the relative hotness orcoldness of objects We need a technical definition of temperature



Thermal Contact Two objects are in thermal contact

with each other if energy can be

exchanged between them The exchanges we will focus on will be in

the form of heat or electromagnetic

radiation The energy is exchanged due to a

temperature difference



Thermal Equilibrium Thermal equilibrium is a situation in

which two objects would not exchange

energy by heat or electromagneticradiation if they were placed in thermalcontact

The thermal contact does not have to alsobe physical contact



Zeroth Law of

Thermodynamics If objects A and B are separately in

thermal equilibrium with a third object

C, then A and B are in thermalequilibrium with each other

Let object C be the thermometer

Since they are in thermal equilibrium witheach other, there is no energy exchangedamong them





Temperature – Definition Temperature can be thought of as the

property that determines whether an

object is in thermal equilibrium withother objects

Two objects in thermal equilibrium witheach other are at the same temperature If two objects have different temperatures,

they are not in thermal equilibrium witheach other



Thermometers A thermometer is a device that is

used to measure the temperature of a

system

Thermometers are based on theprinciple that some physical property of

a system changes as the system’stemperature changes



Thermometers, cont These properties include:

The volume of a liquid

The dimensions of a solid The pressure of a gas at a constant volume

The volume of a gas at a constant pressure

The electric resistance of a conductor

The color of an object

A temperature scale can be established onthe basis of any of these physical properties



Mercury-in glassthermometer

alcohol thermometer

digital thermometer

infrared thermometer



Celsius Scale Proposed by Swedish astronomer Anders

Celsius in 1742

The ice point of water is defined to be 0o C The steam point of water is defined to be

100o C

The length of the column between these twopoints is divided into 100 increments, calleddegrees



Fahrenheit Scale A common scale in everyday use in the

US

Named for Daniel Fahrenheit (1724) Temperature of the ice point is 32oF

Temperature of the steam point is

212oF There are 180 divisions (degrees)

between the two reference points



Absolute Temperature Scale/

Kelvin Scale Proposed by mathematical physicist and engineer

William Thomson, 1st Baron Kelvin in 1848

Absolute zero is used as the basis of the absolutetemperature scale

The size of the degree on the absolute scale isthe same as the size of the degree on the Celsius

scale To convert:

TC = T – 273.15



Absolute Temperature Scale, 2 The absolute temperature scale is now based

on two new fixed points

Adopted by in 1954 by the InternationalCommittee on Weights and Measures

One point is absolute zero

The other point is the triple point of water

This is the combination of temperature and pressurewhere ice, water, and steam can all coexist



Absolute Temperature Scale, 3 The triple point of water occurs at

0.01o C and 4.58 mm of mercury

This temperature was set to be 273.16on the absolute temperature scale

This made the old absolute scale agree

closely with the new one

The units of the absolute scale are kelvins



Absolute Temperature Scale, 4 The absolute scale is also called the Kelvin

scale

The triple point temperature is 273.16 K No degree symbol is used with kelvins

The kelvin is defined as 1/273.16 of thedifference between absolute zero and thetemperature of the triple point of water



Some Examples of Absolute

Temperatures The figure at right gives

some absolutetemperatures at which

various physicalprocesses occur

The scale is logarithmic

The temperature of absolute zero cannot beachieved Experiments have come

close



Comparison of Scales Celsius and Kelvin have the same size

degrees, but different starting points

TC = T – 273.15

Celsius and Fahrenheit have differentsized degrees and different starting

points

F C

932

5T T F



Comparison of Scales, cont To compare changes in temperature

Ice point temperatures 0oC = 273.15 K = 32o F

Steam point temperatures 100oC = 373.15 K = 212o F

C F

5

9T T T



Thermal Expansion Thermal expansion is the increase in the size of an

object with an increase in its temperature

Thermal expansion is a consequence of the change in

the average separation between the atoms in anobject

If the expansion is small relative to the originaldimensions of the object, the change in anydimension is, to a good approximation, proportionalto the first power of the change in temperature



Linear Expansion Assume an object has an initial length L

That length increases by L as the

temperature changes by T We define the coefficient of linear

expansion as

A convenient form is L = a L 0 T

a

0/L LT



Linear Expansion, cont This equation can also be written in

terms of the initial and final conditions

of the object: L f – L i = a L 0 (T f – T i )

The coefficient of linear expansion, a ,

has units of (oC)-1



Some Coefficients



Linear Expansion, final Some materials expand along one dimension,

but contract along another as the

temperature increases Since the linear dimensions change, it follows

that the surface area and volume also changewith a change in temperature

A cavity in a piece of material expands in thesame way as if the cavity were filled with thematerial



Volume Expansion The change in volume is proportional to

the original volume and to the change

in temperature V = b V 0 T

b is the coefficient of volume expansion

For a solid, b 3a This assumes the material is isotropic, the

same in all directions

For a liquid or gas, b is given in the table



Area Expansion The change in area is proportional to

the original area and to the change in

temperature: A = 2a A i T



Bimetallic Strip Each substance has its

own characteristicaverage coefficient of

expansion

This can be made useof in the device shown,called a bimetallic strip

It can be used in athermostat



Water’s Unusual Behavior As the temperature

increases from 0oC to4oC, water contracts Its density increases

Above 4oC, waterexpands with increasingtemperature Its density decreases

The maximum densityof water (1.000 g/cm3)occurs at 4oC



Heat Heat is defined as the transfer of

energy across the boundary of a system

due to a temperature differencebetween the system and itssurroundings

The term heat will also be used torepresent the amount of energytransferred by this method



Units of Heat Historically, the calorie was the unit used for heat

One calorie is the amount of energy transfer necessary toraise the temperature of 1 g of water from 14.5oC to 15.5oC

The “Calorie” used for food is actually 1 kilocalorie

In the US Customary system, the unit is a BTU(British Thermal Unit)

One BTU is the amount of energy transfer necessary to raise

the temperature of 1 lb of water from 63o

F to 64o

F The standard in the text is to use Joules



James Prescott Joule 1818 – 1889

British physicist

Largely self-educated

Some formal education fromJohn Dalton

Research led toestablishment of theprinciple of Conservation of

Energy Determined the amount of

work needed to produce oneunit of energy



Mechanical Equivalent of Heat Joule established the

equivalence betweenmechanical energy and

internal energy His experimental setup

is shown at right

The loss in potentialenergy associated withthe blocks equals thework done by thepaddle wheel on thewater



Mechanical Equivalent of Heat,

cont Joule found that it took approximately 4.18 J

of mechanical energy to raise the water 1oC

Later, more precise, measurementsdetermined the amount of mechanical energyneeded to raise the temperature of waterfrom 14.5oC to 15.5oC

1 cal = 4.186 J

This is known as the mechanical equivalent of heat



Heat Capacity The heat capacity, C, of a particular

sample is defined as the amount of

energy needed to raise the temperatureof that sample by 1oC

If energy Q produces a change of

temperature of T , thenQ = C T



Specific Heat Specific heat, c, is the heat capacity

per unit mass

If energy Q transfers to a sample of asubstance of mass m and thetemperature changes by T , then the

specific heat is



Specific Heat, cont The specific heat is essentially a measure of

how thermally insensitive a substance is to

the addition of energy The greater the substance’s specific heat, the

more energy that must be added to cause aparticular temperature change

The equation is often written in terms of Q :



Some Specific Heat Values

NOTE – Lead andGold have smallest

specific heats



More Specific Heat Values

NOTE – ice andsteam (different forms of H2O) have ~ ½ x thespecific heat of liquid

water.



Sign Conventions If the temperature increases:

Q and T are positive

Energy transfers into the system

If the temperature decreases:

Q and T are negative

Energy transfers out of the system



Specific Heat Varies With

Temperature Technically, the specific heat varies with

temperature

The corrected equation is However, if the temperature intervals are not

too large, the variation can be ignored and ccan be treated as a constant For example, for water there is only about a 1%

variation between 0o and 100oC

These variations will be neglected unlessotherwise stated

f

i

T

T Q m c dT



Specific Heat of Water Water has the highest specific heat of

common materials

This is in part responsible for manyweather phenomena

Moderate temperatures near large bodies

of water Global wind systems

Land and sea breezes



CAUTION: The definition of heat. Remember that dQ does not represent a change in the amount of heatcontained in a body; this is a meaningless

concept. Heat is always energy in transit as aresult of a temperature difference. There is no suchthing as “the amount of heat in a body” .

CAUTION: The meaning of “heat capacity” . The term “heat capacity” is unfortunate because it gives theerroneous impression that a body contains certainamount of heat. Remember, heat is energy intransit to or from a body, not the energy residing inthe body.



Why does a metal rod at 200C feelscolder than a piece of wood at200C?



Why do you feel cold whenyou first step out of a

swimming pool?

Evaporative cooling!





Calorimetry One technique for measuring specific

heat involves heating a material, adding

it to a sample of water, and recordingthe final temperature

This technique is known as

calorimetry A calorimeter is a device in which this

energy transfer takes place



Calorimetry, cont The system of the sample and the water is

isolated

Conservation of energy requires that theamount of energy that leaves the sampleequals the amount of energy that enters thewater

Conservation of Energy gives amathematical expression of this:

Q cold= -Q hot



Example, Calorimetry

Answer =



STEEL INGOT

ALUMINUM INGOT



Phase Changes A phase change is when a substance changes from

one form to another

Two common phase changes are

Solid to liquid (melting)

Liquid to gas (boiling)

During a phase change, there is no change intemperature of the substance

For example, in boiling the increase in internal energy isrepresented by the breaking of the bonds betweenmolecules, giving the molecules of the gas a higherintermolecular potential energy



Latent Heat Different substances react differently to the

energy added or removed during a phasechange Due to their different internal molecular

arrangements

The amount of energy also depends on themass of the sample

If an amount of energy Q is required tochange the phase of a sample of mass m ,

L ≡ Q /m



Latent Heat, cont The quantity L is called the latent heat

of the material

Latent means “hidden” The value of L depends on the substance

as well as the actual phase change

The energy required to change thephase is Q = mL



Latent Heat, final The latent heat of fusion is used when the

phase change is from solid to liquid

The latent heat of vaporization is used whenthe phase change is from liquid to gas

The positive sign is used when the energy istransferred into the system

This will result in melting or boiling The negative sign is used when energy is

transferred out of the system This will result in freezing or condensation



Sample Latent Heat Values







Mechanisms of EnergyTransfer by Heat

We want to know the rate at whichenergy is transferred

There are various mechanismsresponsible for the transfer:

Conduction

Convection Radiation



Conduction

The transfer can be viewed on an atomicscale It is an exchange of kinetic energy between

microscopic particles by collisions The microscopic particles can be atoms, molecules or

free electrons

Less energetic particles gain energy duringcollisions with more energetic particles

Rate of conduction depends upon thecharacteristics of the substance



Conduction, cont.

In general, metals are good thermalconductors They contain large numbers of electrons that are

relatively free to move through the metal They can transport energy from one region to

another

Poor conductors include asbestos, paper, and

gases Conduction can occur only if there is a

difference in temperature between two partsof the conducting medium



Conduction, equation

The slab at right allowsenergy to transfer fromthe region of higher

temperature to theregion of lowertemperature

The rate of transfer is

given by:

Q dT H kA

t dx



Conduction, equationexplanation

A is the cross-sectional area

Δx is the thickness of the slab

Or the length of a rod is in Watts when Q is in Joules and t is in

seconds

k is the thermal conductivity of the material

Good conductors have high k values and goodinsulators have low k values

H



Temperature Gradient

The quantity |dT / dx | iscalled the temperaturegradient of the material

It measures the rate atwhich temperature varieswith position

For a rod, the temperaturegradient can be expressedas:

h cdT T T

dx L



Rate of Energy Transfer in a Rod

Using the temperature gradient for therod, the rate of energy transfer

becomes:

h c T T

H kAL



Compound Slab

For a compound slab containing severalmaterials of various thicknesses (L 1, L 2,

…) and various thermal conductivities(k 1, k 2, …) the rate of energy transferdepends on the materials and the

temperatures at the outer edges:

h c

i i

i

A T T H

L k



Some Thermal Conductivities



More Thermal Conductivities



Home Insulation

Substances are rated by their R values

R = L / k and the rate becomes

For multiple layers, the total R value is the sum of

the R values of each layer

Wind increases the energy loss by conductionin a home

h c

i

i

A T T H R



Convection

Energy transferred by the movement of a substance

When the movement results fromdifferences in density, it is called natural convection

When the movement is forced by a fan ora pump, it is called forced convection



Convection example

Air directly abovethe radiator iswarmed and

expands The density of the

air decreases, and itrises

A continuous aircurrent isestablished



Radiation

Radiation does not require physicalcontact

All objects radiate energy continuouslyin the form of electromagnetic wavesdue to thermal vibrations of theirmolecules

Rate of radiation is given by Stefan’s

law



Stefan’s Law

P = σ AeT4

P is the rate of energy transfer, in Watts

σ = 5.6696 x 10-8 W/m2 . K 4 A is the surface area of the object

e is a constant called the emissivity e varies from 0 to 1

The emissivity is also equal to the absorptivity

T is the temperature in Kelvins

E Ab ti d



Energy Absorption andEmission by Radiation

With its surroundings, the rate at whichthe object at temperature T with

surroundings at T o radiates is P net = σAe (T 4 –T o

4)

When an object is in equilibrium with its

surroundings, it radiates and absorbs atthe same rate

Its temperature will not change



Ideal Absorbers

An ideal absorber is defined as anobject that absorbs all of the energy

incident on it e = 1

This type of object is called a black body

An ideal absorber is also an idealradiator of energy



Ideal Reflector

An ideal reflector absorbs none of theenergy incident on it

e = 0



The Dewar Flask

A Dewar flask is a container designed tominimize the energy losses by

conduction, convection, and radiation Invented by Sir James Dewar (1842 –

1923)

It is used to store either cold or hot

liquids for long periods of time A Thermos bottle is a common household

equivalent of a Dewar flask



Dewar Flask, Details

The space between the wallsis a vacuum to minimizeenergy transfer byconduction and convection

The silvered surfaceminimizes energy transfersby radiation

Silver is a good reflector

The size of the neck isreduced to further minimizeenergy losses

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Phys11 Temperature&Heat